This study aims to explore how teachers from four countries—France, Israel, Italy, and Germany—manage their teaching–learning activity in the context of lockdown due to the COVID-19 pandemic. About 700 teachers from the four countries participated in this study. They were given an online questionnaire that involved 22 open-ended items, in which they were requested to complete the items that were structured taking into account the relationships between teacher, students, mathematics and resources. The qualitative analysis of teachers’ answers was carried out, referring to both the meta-didactical transposition model and Bishop’s framework on values to investigate teachers’ teaching–learning activities and the reasons underlying their choices. The empirical analysis suggests four tasks corresponding to the main challenges that teachers had to face during the time of lockdown: (a) managing distance learning to support students’ learning through specific methodologies; (b) managing distance learning to develop assessment; (c) managing distance learning to support those students that face difficulties and/or are living a difficult situation/developing inclusive teaching; and (d) managing distance learning to exploit its potentialities for fostering typical mathematical processes. The values that motivated the teachers to change their teaching–learning activities are discussed, conclusions of how the time of lockdown affects the mathematics teaching is drawn, and finally, recommendations and insights from this study are shared.

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture about the mathematical relationships embedded in it. The study was guided by the theory of knowledge objectification. We included two rounds of analysis: one, to detect ‘learning focuses’ involved in learning the FTC and to identify the relationship between them; the other, to identify the ways in which students used the tool to become aware of each focus. Data analysis identified nine focuses in the process of learning the FTC. We described these focuses, the relationships between them, and the ways in which students interacted with the tool to characterize the learning trajectory of the FTC.